Single-mode dielectric waveguide

ABSTRACT

This application describes a single-mode dielectric waveguide for guiding electromagnetic wave energy. The guide comprises a low-loss dielectric substrate in which a thin, low-loss, dielectric strip of higher refractive index is embedded. In general, such a guide is capable of supporting a plurality of modes of two orthogonally-polarized families of modes. To limit the waveguide to single-mode operation, the cross-sectional dimensions are limited so that the guide is incapable of supporting modes higher than the fundamental mode of each of the two families of modes. One of two fundamental modes is then supported by either placing a lossy material along one surface of the guiding strip, thereby making the guide much lossier to one of the two fundamental modes or, alternatively, by placing a higher refractive index material along the strip, thereby destroying the guiding capability of the waveguide with respect to one of the two fundamental modes.

u uses, Dldli Related U.S. Appllcatlon Data [63] Continuation-in-part ofSer. No. 730,192, May 17,

1968, abandoned.

[52] US. Cl..... ..350/96 WG [51] Int. Cl ...H0lp 3/00, G021) 5/14 [58]Field of Search ..350/96 WG [56] References Cited UNITED STATES PATENTS3,563,630 2/1971 Anderson et a1. ..350/96 WG 3,350,654 10/1967 Snitzer..350/96 WG UX 2,794,959 6/1957 Fox ..350/96 WG UX 3,386,787 6/1968Kaplan ..350/96 WG OPT/CAL LE 5 SOURCE [1 1 3,659,916 1 May 2, 1972OTHER PUBLICATIONS Schineller Single-Mode-Guide Laser ComponentsMicrowaves Vol. 7, No. 1, Jan. 1968, pp. 77- 85.

Primary Examiner-John K. Corbin Attorney-R. J. Guenther and Arthur J.Torsiglieri 5 7] ABSTRACT This application describes a single-modedielectric waveguide for guiding electromagnetic wave energy. The guidecomprises a low-loss dielectric substrate in which a thin, low-loss,dielectric strip of higher refractive index is embedded. in general,such a guide is capable of supporting a plurality of modes of twoorthogonally-polarized families of modes. To limit the waveguide tosingle-mode operation, the cross-sectional dimensions are limited sothat the guide is incapable of supporting modes higher than thefundamental mode of each of the two families of modes. One of twofundamental modes is then supported by either placing a lossy materialalong one surface of the guiding strip, thereby making the guide muchlossier to one of the two fundamental modes or, alternatively, byplacing a higher refractive index material along the strip, therebydestroying the guiding capability of the waveguide with respect to oneof the two fundamental modes.

5 Claims, 11 Drawing Figures APPARATUS Patented May 2, 1972 3Sheets-Sheet 2 A FIG. 3F FIG. 3

26 20 z 22 l L l i I & 7

Patented May 2, 1972 3,659,916

3 SheetsSheet 5 FIG. 4

FIG. 5

nfl-A) SINGLE-MODE DIELECTRIC WAVEGUIDE This invention, which relates tosingle-mode dielectric waveguides, is a continuation-in-part of mycopending application Ser. No. 730,192, filed May 17, 1968, nowabandoned.

BACKGROUND OF THE INVENTION In the transmission of electromagnetic waveenergy through a hollow conductive pipe or other type of waveguide, itis well known that the energy can propagate in one or more transmissionmodes, or characteristic field configurations, depending upon thecross-sectional size and shape of the particular guide, and upon theoperating frequency. Typically, at any given frequency, the larger theguide size the greater are the number of modes in which the energy canpropagate. Normally, it is desired to confine propagation to oneparticular mode chosen because its propagation characteristics arefavorable for the particular application involved, and becausepropagation in more than one mode gives rise to power loss,conversionreconversion distortion and other deleterious effects.

If the desired mode happens to be the so-called dominant mode, and thewavelength of the wave energy is large enough, it is feasible torestrict the cross-sectional dimensions of the guide so that no modesother than the dominant mode can be sustained therein. This expedient isnot applicable, however, if the desired mode is not the dominant mode,or if a guide of larger cross section is prescribed in order to minimizeattenuation or for other reasons. These oversized, or multimodewaveguides, are inherently capable of propagating more than one modeand, as such, are potentially troublesome. In these instances it becomesnecessary to go to more complicated waveguiding structures such as, forexample, the helical waveguide.

The advent of the optical maser as a source of coherent radiation atoptical wavelengths has substantially magnified the problems of guidingelectromagnetic wave energy. Because of the extremely small wavelengthsinvolved, none of the techniques considered above have heretoforeprovided a practical means of obtaining efficient transmission.

In an article entitled Optical Waveguide of Macroscopic Dimensions inSingle Mode Operation" by R. A. Kaplan, published in the Aug. 1963 issueof the Proceedings of the Inslitute of Electrical and ElectronicEngineers and, more recently, in an article by E. R. Schineller entitled"Single- Mode-Guide Laser Components," published in the Jan. 1968 issueof Microwaves, it is suggested that a dielectric waveguide, having aparticular thickness, will limit propagation to the fundamental mode. Inparticular, the structure disclosed comprises a dielectric core embeddedin a transparent dielectric medium of slightly lower dielectricconstant. The core is typically a thin slab of prescribed thickness, butof undefined width.

Further study of this type of waveguide, however, has revealed that themode-supporting properties of such a structure are more complex thanthat suggested in the aboveidentified articles.

SUMMARY OF THE INVENTION The present invention is based upon therecognition that a dielectric waveguide is capable of supporting pairsof orthogonally-polarized families of modes. Thus, if a dielectricwaveguide is to be truly supportive of only a single propagating mode,both transverse dimensions must be defined within specified limits.

In accordance with the present invention, single-mode propagation alonga dielectric wav eguide comprising a guiding strip of essentiallyrectangular cross section, is achieved y selecting both transversedimensions of the dielectric guiding strip so as to limit guidance to nohigher than the fundamental mode of each of the twoorthogonally-polarized family of modes, and including means for eitherattenuating or preventing guidance of one of the two fundamental modes.In one embodiment of the invention, to be described in greater detailhereinbelow, the waveguide is made very much lossier to one of the twoorthogonally-polarized fundamental modes by placing a lossy material, oflower refractive index than the strip, along one surface of the guidingstrip. in a second embodiment of the invention, all the modes in thefamily of modes to be suppressed are made evanescent by locating ahigher refractive index material along one side of the guiding strip.

One of the principal advantages of the present invention resides in thefact that it is a physically realizable structure. The importance ofthis is illustrated by reference to U.S. Pat. No. 3,386,787, which alsoshows a form of mode-limited waveguide comprising two, coaxialdielectric cylinders, bisected by means of a conductive surface. In sucha waveguide, however, the ratio of the cross-sectional dimensions of theguiding strip is fixed at two-to-one; and while such a waveguidingstructure is theoretically capable of singlemode operation, there arepractical difficulties associated with its construction. For example,the invention contemplates fabricating dielectric waveguides bydifiusing an impurity into a substrate, using a masking process, to forma thin, film-like guiding strip. The depth r of the diffusion wouldtypically be a few tenths of a micron, and can be readily controlled bywellknown techniques. However, it is beyond the state of the art to makea mask having an opening whose width is comparable to I since theirregularities along the edges of the mask opening would themselves becomparable to the r dimension. As a practical matter, the width w of theguiding strip, as contemplated by the present invention, will,typically, be larger than 2!. Specifically, widths of the order of fouror more times greater than I appear useful.

Thus, it can be anticipated that a guide configuration which limits thestrip width to twice the strip thickness will be very lossy for thereasons noted. By contrast, the present invention discloses a dielectricwaveguide comprising a guiding strip having an essentially rectangularcross-sectional configuration which is limited to single-modepropagation over an infinite range of width-to-thickness ratios.

These and other objects and advantages, the nature of the presentinvention, and its various features, will appear more fully uponconsideration of the various illustrative'embodiments now to bedescribed in detail in connection with the accompanying drawing.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. I shows an optical systemincluding a dielectric waveguide;

FIG. 2 shows a first embodiment of a dielectric waveguide in accordancewith the invention;

FIGS. 3A through 3G, included for'purposes of explanation, show adielectric waveguide and the electric field configurations along twomutually perpendicular directions transverse to the direction of wavepropagation;

FIG. 4 shows the effect upon the field configuration produced by placinga high admittance material adjacent to one side of the waveguide strip;and

FIG. 5 shows an alternate embodiment of the invention wherein therefractive index of the substrate material in contact with the guidingstrip is not the same along all sides.

DETAILED DESCRIPTION While, in principle, the invention can be used toguide electromagnetic wave energy at any frequency, the folk wingdiscussion is directed specifically to the guidance of optical waveenergy including wave energy in the infrared, the visible and theultraviolet portions of the frequency spectrum. In this connection, FIG.1 shows an optical system including a source 1 of optical wave energy,and a lens system 2 for focusing and directing the wave energy emittedfrom source 1 onto one end of a diskQELQEYeguide 3 of the type to bedescribed in greater detail hereinbelow.

At the output end of waveguide 3, a second lens system 4 directs andfocuses the wave energy from guide 3 into some form of outpututilization apparatus 5.

FIG. 2 shows dielectric waveguide 3, in accordance with the presentinvention, comprising a transparent (low-loss) dielectric strip I0, ofrefractive index n, embedded in a second transparent dielectric material11, such as glass, of slightly lower refractive index n( l-A).

While the permissible cross-sectional dimensions of strip will bedefined in greater detail hereinbelow. it is contemplated, in accordancewith the present invention, that strip 10 is a thin film or ribbon-likemember whose thickness 1 is much less than its width w. Typically, apreferred width-to-thickness ratio is of the order of 4 to l or greater.

Disposed along the exposed (upper) side of strip 11, and in contacttherewith, is a layer of a third material 12 whose properties will bediscussed in greater detail hereinbelow.

For purposes of illustration, and to simplify the mathematicalcalculations, strip 10 is shown to have a precisely rectangular crosssection. This, however, is not at all essential to the operation of theinvention, nor is it very likely to be so. In general, while thecross-sectional configuration of strip 10 is essentially rectangular,its exact configuration will depend upon the particular manufacturingprocess employed. Typically, the edges of the strip will either berounded off, causing the cross section of the guiding strip to assume amore elliptical shape, or the edges will be irregular. In addition, therefractive index, typically, will not change abruptly but, rather, willtaper from one value in one dielectric material to a second value in anadjacent material. Notwithstanding these departures from the idealizedconfiguration, the operation of the waveguide is in accordance with theprinciples to be considered, and the actual strip dimensions areessentially, if not exactly, as defined hereinbelow.

Before proceeding with a discussion of the invention, some generalcomments about the field distribution in a dielectric waveguide,comprising dissimilar dielectric materials, would appear to be helpful.Accordingly, FIG. 3A through FIG. 3G are included for purposes ofexplanation. Specifically, FIG. 3A shows the cross section of adielectric waveguide comprising, as in FIG. 2, a guiding strip embeddedin a substrate 21 of slightly lower dielectric constant. For purposes ofthe following discussion, the upper surface of strip 20 is depicted asin contact with a material 26 whose refractive index N, is lower thanthat of strip 20 and substrate 21. As an example, material 26 can be airfor which n I.

In general, the modes that propagate along strip 20 are characterized byelectric and magnetic field distributions that include components alongthe direction of propagation and along two mutually-perpendiculardirections transverse to the direction of propagation. However, sincethe axial components are very much smaller than the transversecomponents, the former are neglected in the discussion that follows, andonly the transverse components are referred to. Thus, the modes may beconveniently divided into two families whose electric fields arepolarized along two mutually-perpendicular directions transverse to thedirection of wave propagation. In FIG. 3A, one of these directions,normal to the strip-air interface 22, is designated the y direction, andthe other direction, parallel to the strip-air interface is designatedthe x direction.

FIGS. 38 through 3D depict, qualitatively, the electric fielddistributions of the three lowest order propagating modes for bothfamilies of modes that can be supported by a guiding strip of width w.FIG. 3B shows a higher order mode which, for purposes of illustration,is shown as an evanescent, or nonguided mode.

Basically, each of the modes for both families of orthogonally-polarizedmodes, is characterized by a sinusoidal varying field distributionwithin guiding strip 20 along both the x and y directions, and byexponentially decreasing field distributions in substrate 21 and in thesurrounding air. Thus, referring more specifically to FIG. 3B, thelowest order EH mode is characterized by a sinusoidally varying fielddistribution 30 within strip 20 in the x direction of less than one-halfguide wavelength, where a guide wavelength, A, for the 0 order mode inthe x direction is given by and by exponentially decreasing fielddistributions 3! and 32 in substrate 21. Because of the symmetry of thestructure about the y direction axis, the amplitude of the fielddistribution is symmetrical with respectto the guidec enter.

The field distribution in the y direction, shown in FIG. 3F, (where q I0) is similar to the field distribution in the x direction in that itincludes a sinusoidally varying region 70 and exponential regions 71 and72. However, because the dielectric materials above and below guidestrip 20 are different, the field distribution in the y direction is notsymmetric with respect to the center of strip 20. Instead, there is adisplacement towards the higher dielectric material which, in FIG. 3A,is the material of substrate 21. This is clearly indicated in FIG. 3Fwhich shows the peak amplitude of the sinusoidal portion of the fielddistribution 70 displaced towards the guide-substrate interface 23 and,correspondingly, displaced away from the guide-air interface 22. Theexponentially decreasing portions 71 and 72 of the field distributionare correspondingly dissimilar, with a larger proportion of theelectromagnetic wave energy being distributed in the substrate, and lessin the air.

In order for any mode to be guided, guide strip 20 must be capable ofsupporting the field distributions for that particular mode along boththe x and y directions. Assuming materials of equal magneticpermeability, such support is realized when both the slopes (firstderivatives) and the amplitudes of the sinusoidal and exponentialmagnetic fields are equal at the interfaces between the guiding strip 20and the surrounding materials. This is clearly the case for each of thefield distributions illustrated in FIGS. 38 and SF and, hence, thefundamental EH mode for both families of orthogonally-polarized modes iscapable of being guided by and propagates along strip 20.

A similar situation is depicted for the next two higher order modes (EHand EI-I,,,) illustrated in FIGS. 3C and 3D. In each instance, asinusoidally varying field distribution (40 and 50) within strip 20meets the exponential field distributions (4!, 42 and 51, 52),respectively, with the proper am'plitude and slope.

In like fashion, the order of the modes that can be supported along they direction is limited by the thickness, 1, of the guiding strip. Forpurposes of illustration, the guiding strip is assumed to be too thin tosupport any higher order modes. Hence, the next higher order mode(EI-I,,) along the y direction, illustrated in FIG. 36, is shown to bediscontinuous at interface 23 and, hence, unguided. Thus, for purposesof explanation, each of the guided modes EI-I,,,,, Iii-I and EH arecharacterized by a field distribution along the x direction as shown inFIGS. 3B, 3C and 3D, and a field distribution along the y direction asshown in FIG. 3F, in which case q 0.

For the EH, mode, illustrated in FIG. 35, the guiding strip 20 is toonarrow, and a rising field distribution 61 and 62 at each interface 22and 23 makes it impossible to satisfy the equal slope requirements of aguided mode. As a result, energy coupled into the 5H,. mode, or anyhigher order mode, is not guided along strip 20, but tends to spreadthroughout the substrate. Such a mode is referred to as an unguidedmode.

From the above discussion it is evident that for a mode to be guided,the guiding strip must be large enough to support the necessary fielddistribution along two mutually perpendicular transverse directions.This further means that at the very least, the guide will support thefundamental mode for each of the two orthogonally-polarized families ofmodes. Hence, in the absence of any special precautions, a dielectricwaveguide cannot be a single mode waveguide. The higher order modes,however, can readily be suppressed by restricting the crosssectionaldimensions of the guiding strip. In particular, to limit the waveguideto the fundamental modes, the width, w, and the thickness, 1, of theguiding strip for the above-described waveguide, are such that:

It will be noted. from equation 2), that there is no theoretical lowerlimit to the width of the guide strip. This is so because of thesymmetry of the field distribution, as shown in FIG. 3B, which makes italways possible to equate the slopes of the sinusoidal and exponentialmagnetic fields at the interfaces for any width strip. The thickness ofthe guiding strip, on the other hand, is influenced by the fact that thefield distribution is not symmetrical and, if made less than that givenby equation (3), will not satisfy the field conditions at interface 23.

If, however, the refractive index n, of material 26 is approximatelyequal to the refractive index n(1-A) of the substrate 43, equation (3)also reduces to Having defined the guide strip size so as to supportonly the two orthogonally-polarized fundamental modes, means are nowprovided to suppress one of these two modes and, thereby, to realizesingle mode propagation. In particular, there are two possibleapproaches that can be employed, as are now described.

1. Lossy dielectric material with refractive index lml In in accordancewith this first embodiment of the invention, a layer of lossy materialis placed in contact with one of the surfaces of the guiding strip.Thus, for this embodiment, layer 12 in H6. 2 is a material that is lossyover the frequency of interest. For the mode whose electric field isprimarily directed normal to interface 13, between strip and lossymaterial 12, the energy loss due to the presence of layer 12 isrelatively small. However, for the mode that is primarily polarizedparallel to interface 13, the loss is significant, and that mode is moreheavily attenuated. This arrangement is similar to the helicalwaveguide, as used as millimeter wave frequencies, wherein the TM modesare more highly attenuated by the lossy jacket surrounding the helicalstructure than is the desired circular electric mode wave.

it is recognized that the term lossy" is a relative term and, hence,some standard against which loss is measured must be established. Since,as indicated above, both modes are attenuated by the lossy layer, thelevel of loss to be introduced is preferably measured by the effect uponthe desired mode, rather than by the effect upon the mode to beeliminated. As a practical matter, a doubling of the attenuationconstant of the desired mode would appear to be acceptable. However, agreater or smaller change in the attenuation constant may be decidedupon, depending upon the particular application. In any case, theundesired mode, by experiencing a much higher level of attenuation, is,for all practical purposes, suppressed.

It should be noted that in this arrangement, both orthogonal modes aresupported by, and propagated along the guide. The strip dimensions aredefined within the limits given by equations (2) and (3).

Lossy strip 12 is conveniently made of the same material as substrate11, additionally doped with some metallic ions, such as cobalt or iron,to realize the desired level of attenuation.

2. Higher admittance material with [ri l n In accordance with a secondembodiment of the invention, single-mode operation is realized byplacing a high admittance material, having a larger refractive indexthan the strip, along one of the surfaces of the strip.

Since the admittance Yet a material is given by and e. is the dielectricconstant of free space, the desired mode suppression is realized.

It should be noted, in this connection, that by "large" is meant two,three or more times greater than the refractive index of the guidingstrip. That is, the absolute value In, of the refractive index of thematerial of layer 12 is equal to or greater than [2n]. However, as willbe explained in greater detail hereinbelow, larger refractive indicesare to be preferred. Thus, this material can either be a metal. or asemiconductor material such as intrinsic gallium arsenide.

The effect of locating a high admittance material along the guidingstrip is to alter the field distributions along the y direction for thetwo differently-polarized modes in a manner which renders the undesiredmode unguided, while the desired mode remains a guided mode. This isillustrated in FIG. 4 which shows the electric field distributions alongthe y direction for the x and y-polarized modes. When the admittance oflayer 12 is much larger than that of the guiding strip, the electricfield intensity for the x-polarized mode is essentially zero atinterface 13. It increases sinusoidally and, with the strip thicknessless than a quarter of a guide wavelength, where a guide wavelength, A,,in the y direction is given essentially by X nvfi A the field intensityis rising and reaches a maximum at interface 14. Since the slope of thefield within strip 10 is increasing while the slope in substrate 11 isdecreasing, the equal slope conditions cannot be satisfied at interface14, and the mode becomes unguided.

For the y-polarized mode, however, the electric field is close to amaximum at interface 13, increases to a maxim um within the guide strip,and then decreases to a lower value at interface 13. For the limitingcase where n, the field is a maximum at interface 13. However, in allcases the equal slope condition can be satisfied at both interfaces andthe ypolarized wave remains a guided wave.

The attenuation per unit length for the y-polarized wave is given by:

where 1m refers to the imaginary part of the expression within theparenthesis.

From equation 8) it is seen that the attenuation of the preferred modedecreases as n, increases. Thus, the material used in layer 12,advantageously, has a very large admittance at the frequency ofinterest. As an example, a metal, whose admittance at the frequency ofinterest is one order of magnitude greater than that of the waveguide,is advantageously used.

in the embodiment of FIG. 2 guiding strip 10 is partially embedded in asubstrate 11 of unifonn refractive index n( l-A). However, since thetransverse dimensions w and r of the guiding strip depend upon thedifference in refractive index between the strip and the surroundingmedia, a greater range of strip aspect ratios can be realized by meansof the arrangement illustrated in FIG. wherein the substrate material 40and 41 along the r dimension of the strip 42 is not the same as thematerials 43 and 44 along the w dimensions of strip 42.

An important advantage of the embodiment of FIG. 5 is that it permits agreater range of width-to-thickness ratios than can be realized with auniform substrate. That is. wider strips supportive of only thefundamental mode of propagation can be made by using a refractive indexmaterial along the narrow sides of the strip such that A A.

While the invention has been described with particular reference to thepropagation of electromagnetic wave energy in the optical range, it isunderstood that the dielectric waveguide described herein can also beused to guide wave energy in the microwave and millimeter wave portionsof the spectrum. Thus, in all cases it is understood that the abovedescribed arrangements are illustrative of a small number of the manypossible specific embodiments which can represent applications of theprinciples of the invention. Numerous and varied other arrangements canreadily be devised in accordance with these principles by those skilledin the art without departing from the spirit and scope of the invention.

Iclairn:

l. A waveguide for guiding electromagnetic wave energy comprising:

an elongated, low-loss dielectric guiding strip, having a refractiveindex n and an essentially rectangular cross section, embedded in alow-loss dielectric substrate of lower refractive index;

said substrate contacting the two narrow surfaces and one of the widesurfaces of said strip;

and a high admittance material having a refractive index whose magnitudeis larger than the refractive index of said strip contacting the otherwide surface of said strip;

characterized in that:

the narrow dimension r and the wide dimension w of said strip are givenby and en where the refractive index of the portion of substrate incontact with said narrow surfaces is n( l A the refractive index of theportion of substrate in contact with said one wide surface is n(l A),and A is the free space wavelength of said wave energy.

2. The waveguide according to claim 1 wherein A is smaller than A.

3. The waveguide according to claim 1 wherein A A. 4. The waveguideaccording to claim 1 wherein said material is a metal.

5. The waveguide according to claim 1 wherein said material is asemiconductor UNITED STATES PATENT OFFICE v CERTIFICATE OF CQREC'NQNPatent No. 3, 59, 9 Dated. May 97 Inventor(s) Enrique A J Marcatili Itis certified that error appears in the above-identified patent and thatsaid Letters Patent are hereby corrected as shown below:

- 1. is F I V "1* I r Col. l, line 2, change U1 to l,.[[

I c V H 7\ H Col. 8, line 13, change L Lo At the end of claim 5 put a.period.

Signed and sealed this 28th day of November 1972.

EDWARD IVLFLETCHER JR RUBER Attesting Officer T GUTESCHALK Commissionerof Patents FORM FO-105O (10-69) JbCOMM-DC 60376-7 69 u S, GOVFRNMINTPmmmr, ()FHCL 106'; 0-166-3'14

1. A waveguide for guiding electromagnetic wave energy comprising: anelongated, low-loss dielectric guiding strip, having a refractive indexn and an essentially rectangular cross section, embedded in a low-lossdielectric substrate of lower refractive index; said substratecontacting the two narrow surfaces and one of the wide surfaces of saidstrip; and a high admittance material having a refractive index whosemagnitude is larger than the refractive index of said strip contactingthe other wide surface of said strip; characterized in that: the narrowdimension t and the wide dimension w of said strip are given by andwhere the refractive index of the portion of substrate in contact withsaid narrow surfaces is n(1 - Delta ''), the refractive index Of theportion of substrate in contact with said one wide surface is n(1 -Delta ), and lambda is the free space wavelength of said wave energy. 2.The waveguide according to claim 1 wherein Delta '' is smaller thanDelta .
 3. The waveguide according to claim 1 wherein Delta '' Delta .4. The waveguide according to claim 1 wherein said material is a metal.5. The waveguide according to claim 1 wherein said material is asemiconductor